where M is the rocket mass, ΔvR is the increase in velocity of the rocket in a short time interval, Δt, m° is the rate of mass discharge in the exhaust, ve is the effective exhaust velocity (nearly equal to the jet velocity and taken relative to the rocket), and F is force. The quantity m°ve is the propulsive force, or thrust, produced on the rocket by exhausting the propellant,

Evidently thrust can be made large by using a high mass discharge rate or high exhaust velocity. Employing high m° uses up the propellant supply quickly (or requires a large supply), and so it is preferable to seek high values of ve. The value of ve is limited by practical considerations, determined by how the exhaust is accelerated in the supersonic nozzle and what energy supply is available for the propellant heating.

Most rockets derive their energy in thermal form by combustion of condensed-phase propellants at elevated pressure. The gaseous combustion products are exhausted through the nozzle that converts most of the thermal energy to kinetic energy. The maximum amount of energy available is limited to that provided by combustion or by practical considerations imposed by the high temperature involved. Higher energies are possible if other energy sources (e.g., electric or microwave heating) are used in conjunction with the chemical propellants on board the rockets, and extremely high energies are achievable when the exhaust is accelerated by electromagnetic means.

The effective exhaust velocity is the figure of merit for rocket propulsion because it is a measure of thrust per unit mass of propellant consumed—i.e.,

Values of ve are in the range 2,000–5,000 metres (6,500–16,400 feet) per second for chemical propellants, while values two or three times that are claimed for electrically heated propellants. Values beyond 40,000 metres (131,000 feet) per second are predicted for systems using electromagnetic acceleration. In engineering circles, notably in the United States, the effective exhaust velocity is widely expressed in units of seconds, which is referred to as specific impulse. Values in seconds are obtained by dividing the effective exhaust velocities by the constant factor 9.81 metres per second squared (32.2 feet per second squared).

In a typical chemical-rocket mission, anywhere from 50 to 95 percent or more of the takeoff mass is propellant. This can be put in perspective by the equation for burnout velocity (assuming gravity-free and drag-free flight),

In this expression, Ms/Mp is the ratio of propulsion system and structure mass to propellant mass, with a typical value of 0.09 (the symbol ln represents natural logarithm). Mp/Mo is the ratio of propellant mass to all-up takeoff mass, with a typical value of 0.90. A typical value for ve for a hydrogen–oxygen system is 3,536 metres (11,601 feet) per second. From the above equation, the ratio of payload mass to takeoff mass (Mpay/Mo) can be calculated. For a low Earthorbit, vb is about 7,544 metres (24,751 feet) per second, which would require Mpay/Mo to be 0.0374. In other words, it would take a 1,337,000-kg (2,948,000-pound) takeoff system to put 50,000 kg (110,000 pounds) in a low orbit around Earth. This is an optimistic calculation because equation (4) does not take into account the effect of gravity, drag, or directional corrections during ascent, which would noticeably increase the takeoff mass. From equation (4) it is evident that there is a direct trade-off between Ms and Mpay, so that every effort is made to design for low structural mass, and Ms/Mp is a second figure of merit for the propulsion system. While the various mass ratios chosen depend strongly on the mission, rocket payloads generally represent a small part of the takeoff mass.

Pegasus: Pegasus XLNASAA technique called multiple staging is used in many missions to minimize the size of the takeoff vehicle. A launch vehicle carries a second rocket as its payload, to be fired after burnout of the first stage (which is left behind). In this way, the inert components of the first stage are not carried to final velocity, with the second-stage thrust being more effectively applied to the payload. Most spaceflights use at least two stages. The strategy is extended to more stages in missions calling for very high velocities. The U.S. Apollo manned lunar missions used a total of six stages.

The unique features of rockets that make them useful include the following:

1. Rockets can operate in space as well as in the atmosphere of Earth.

2. They can be built to deliver very high thrust (a modern heavy space booster has a takeoff thrust of 3,800 kilonewtons (850,000 pounds).

3. The propulsion system can be relatively simple.

4. The propulsion system can be kept in a ready-to-fire state (important in military systems).

5. Small rockets can be fired from a variety of launch platforms, ranging from packing crates to shoulder launchers to aircraft (there is no recoil).

These features explain not only why all speed and distance records are set by rocket systems (air, land, space) but also why rockets are the exclusive choice for spaceflight. They also have led to a transformation of warfare, both strategic and tactical. Indeed, the emergence and advancement of modern rocket technology can be traced to weapon developments during and since World War II, with a substantial portion being funded through “space agency” initiatives such as the Ariane, Apollo, and space shuttle programs.

Click anywhere inside the article to add text or insert superscripts, subscripts, and special characters.
You can also highlight a section and use the tools in this bar to modify existing content:

Add links to related Britannica articles!
You can double-click any word or highlight a word or phrase in the text below and then select an article from the search box.
Or, simply highlight a word or phrase in the article, then enter the article name or term you'd like to link to in the search box below, and select from the list of results.

Note: we do not allow links to external resources in editor.
Please click the Web sites link for this article to add citations for
external Web sites.